Polygons 180(n-2) formula logic

[KICKGMATASS123]

If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.

Please explain this in detail i dont understand the approach to do this kind of question

Thanks
OA is A

[DeepakR]

Sum of interior angles of a polygon = (n-2) * 180
Where n is the number of sides. Given that n < 9

#1. It states that (n-2)*180/16 is an integer. This gets satisfied only for n=6
then 4*180/16 = 45. So n=6. Hence A is sufficient.

#2. It states that (n-2)*180/15 = integer. For this condition all the values of n like n=3,4,5 will satisfy. So we cant conclusively say the value of n. Hence B is insufficient.

Hence A.) alone is sufficient.

- Deepak

[aj5105]

(A)